"… Kuhn was trying to understand how Aristotle could be such a brilliant natural scientist except when it came to understanding motion. Aristotle's idea that stones fall and fire rises because they're trying to get to their natural places seems like a simpleton's animism.

Then it became clear to Kuhn all at once. Ever since Newton, we in the West have thought movement changes an object's position in neutral space but does not change the object itself. For Aristotle, a change in position was a change in a quality of the object, and qualitative change tended toward an asymmetric actualization of potential: an acorn becomes an oak, but an oak never becomes an acorn. Motion likewise expressed a tendency for things to actualize their essence by moving to their proper place. With that, 'another initially strange part of Aristotelian doctrine begins to fall into place,' Kuhn wrote in The Road Since Structure ."

"… these tools cannot be immediately applied within our current workplaces, educational systems, and public management systems because the operation of these systems is determined, not by personal developmental or societal needs, but by a range of latent, rarely discussed, and hard to influence sociological forces.

But this is not a cry of despair: It points to another topic which has been widely neglected by psychologists: It tells us that human behaviour is not mainly determined by internal properties— such as talents, attitudes, and values— but by external social forces. Such a transformation in psychological thinking and theorising is as great as the transformation Newton introduced into physics by noting that the movement of inanimate objects is not determined by internal, 'animistic,' properties of the objects but by invisible external forces which act upon them— invisible forces that can nevertheless be mapped, measured, and harnessed to do useful work for humankind.

So this brings us to our fourth conceptualisation and measurement topic: How are these social forces to be conceptualised, mapped, measured, and harnessed in a manner analogous to the way in which Newton made it possible to harness the destructive forces of the wind and the waves to enable sailing boats to get to their destinations?"

… There is a Cave
Within the Mount of God, fast by his Throne,
Where light and darkness in perpetual round
Lodge and dislodge by turns, which makes through Heav'n
Grateful vicissitude, like Day and Night….

If Galois geometry is thought of as a paradigm shift from Euclidean geometry,
both images above— the Kuhn cover and the nine-point affine plane—
may be viewed, taken together, as illustrating the shift. The nine subcubes
of the Euclidean 3×3 cube on the Kuhn cover do not form an affine plane
in the coordinate system of the Galois cube in the second image, but they
at least suggest such a plane. Similarly, transformations of a
non-mathematical object, the 1974 Rubik cube, are not Galois transformations,
but they at least suggest such transformations.

See also today's online Harvard Crimson illustration of problems of translation—
not unrelated to the problems of commensurability discussed by Kuhn.

Thursday, February 17, 2011

"These passages suggest that the Form is a character or set of characters
common to a number of things, i.e. the feature in reality which corresponds
to a general word. But Plato also uses language which suggests not only
that the forms exist separately (χωριστά ) from all the particulars, but also
that each form is a peculiarly accurate or good particular of its own kind,
i.e. the standard particular of the kind in question or the model (παράδειγμα )
[i.e. paradigm ] to which other particulars approximate….

… Both in the Republic and in the Sophist there is a strong suggestion
that correct thinking is following out the connexions between Forms.
The model is mathematical thinking, e.g. the proof given in the Meno
that the square on the diagonal is double the original square in area."

— William and Martha Kneale, The Development of Logic,
Oxford University Press paperback, 1985

Some pedagogues may find handling all of these
conceptual changes simultaneously somewhat difficult.

* "Paradigmshift " is a phrase that, as John Baez has rightly pointed out,
should be used with caution. The related phrase here was suggested by Plato's
term παράδειγμα above, along with the commentators' specific reference to
the Meno figure that serves as a model. (For "model" in a different sense,
see Burkard Polster.) But note that Baez's own beloved category theory
has been called a paradigm shift.

Comments Off on Paradigms

Saturday, September 30, 2017

"Origin is Mr. Brown’s eighth novel. It finds his familiar protagonist,
the brilliant Harvard professor of symbology and religious iconography
Robert Langdon, embroiled once more in an intellectually challenging,
life-threatening adventure involving murderous zealots, shadowy fringe
organizations, paradigm-shifting secrets with implications for the future
of humanity, symbols within puzzles and puzzles within symbols and
a female companion who is super-smart and super-hot.

As do all of Mr. Brown’s works, the new novel does not shy away from
the big questions, but rather rushes headlong into them."

Saturday, July 26, 2014

The philosopher Graham Harman is invested in re-thinking the autonomy of objects and is part of a movement called Object-Oriented-Philosophy (OOP). Harman wants to question the authority of the human being at the center of philosophy to allow the insertion of the inanimate into the equation. With the aim of proposing a philosophy of objects themselves, Harman puts the philosophies of Bruno Latour and Martin Heidegger in dialogue. Along these lines, Harman proposes an unconventional reading of the tool-being analysis made by Heidegger. For Harman, the term tool does not refer only to human-invented tools such as hammers or screwdrivers, but to any kind of being or thing such as a stone, dog or even a human. Further, he uses the terms objects, beings, tools and things, interchangeably, placing all on the same ontological footing. In short, there is no “outside world.”

Harman distinguishes two characteristics of the tool-being: invisibility and totality. Invisibility means that an object is not simply used but is: “[an object] form(s) a cosmic infrastructure of artificial and natural and perhaps supernatural forces, power by which our last action is besieged.” For instance, nails, wooden boards and plumbing tubes do their work to keep a house “running” silently (invisibly) without being viewed or noticed. Totality means that objects do not operate alone but always in relation to other objects–the smallest nail can, for example, not be disconnected from wooden boards, the plumbing tubes or from the cement. Depending on the point of view of each entity (nail, tube, etc.) a different reality will emerge within the house. For Harman, “to refer to an object as a tool-being is not to say that it is brutally exploited as a means to an end, but only that it is torn apart by the universal duel between the silent execution of an object’s reality and the glistening aura of its tangible surface.”

— From “The Action of Things,” an M.A. thesis at the Center for Curatorial Studies, Bard College, by Manuela Moscoso, May 2011, edited by Sarah Demeuse

Sunday, July 20, 2014

The discovery of the incommensurability of a square's
side with its diagonal contrasted a well-known discrete
length (the side) with a new continuous length (the diagonal).
The figures below illustrate a shift in the other direction.
The essential structure of the continuous configuration at
left is embodied in the discrete unit cells of the square at right.

"Just because it is a transition between incommensurables, the transition between competing paradigms cannot be made a step at a time, forced by logic and neutral experience. Like the gestalt switch, it must occur all at once (though not necessarily in an instant) or not at all."

"In the spiritual traditions from which Jung borrowed the term, it is not the SYMMETRY of mandalas that is all-important, as Jung later led us to believe. It is their capacity to reveal the asymmetry that resides at the very heart of symmetry."

I have little respect for Enneagram enthusiasts, but they do at times illustrate Mailer's maxim.

My own interests are in the purely mathematical properties of the number nine, as well as those of the next square, sixteen.

Those who prefer bullshit may investigate non-mathematical properties of sixteen by doing a Google image search on MBTI.

For bullshit involving nine, see (for instance) Einsatz in this journal.

For non-bullshit involving nine, sixteen, and "asymmetry that resides at the very heart of symmetry," see Monday's Mapping Problem continued. (The nine occurs there as the symmetric figures in the lower right nine-sixteenths of the triangular analogs diagram.)

For non-bullshit involving psychological and philosophical terminology, see James Hillman's Re-Visioning Psychology.

Friday, June 22, 2012

A professor of philosophy in 1984 on Socrates's geometric proof in Plato's Meno dialogue—

"These recondite issues matter because theories about mathematics have had a big place in Western philosophy. All kinds of outlandish doctrines have tried to explain the nature of mathematical knowledge. Socrates set the ball rolling…."

— Ian Hacking in The New York Review of Books , Feb. 16, 1984

The same professor introducing a new edition of Kuhn's Structure of Scientific Revolutions—

"That is the structure of scientific revolutions: normal science with a paradigm and a dedication to solving puzzles; followed by serious anomalies, which lead to a crisis; and finally resolution of the crisis by a new paradigm. Another famous word does not occur in the section titles: incommensurability. This is the idea that, in the course of a revolution and paradigm shift, the new ideas and assertions cannot be strictly compared to the old ones."

The Meno proof involves inscribing diagonals in squares. It is therefore related, albeit indirectly, to the classic Greek discovery that the diagonals of a square are incommensurable with its sides. Hence the following discussion of incommensurability seems relevant.

See also von Fritz and incommensurability in The New York Times (March 8, 2011).

For mathematical remarks related to the 10-dot triangular array of von Fritz, diagonals, and bowling, see this journal on Nov. 8, 2011— "Stoned."

Comments Off on Bowling in Diagon Alley

Monday, May 28, 2012

Jamie James in The Music of the Spheres(Springer paperback, 1995), page 28—

Pythagoras constructed a table of opposites
from which he was able to derive every concept
needed for a philosophy of the phenomenal world.
As reconstructed by Aristotle in his Metaphysics,
the table contains ten dualities….

Limited
Odd
One
Right
Male
Rest
Straight
Light
Good
Square

Unlimited
Even
Many
Left
Female
Motion
Curved
Dark
Bad
Oblong

Of these dualities, the first is the most important;
all the others may be seen as different aspects
of this fundamental dichotomy.

The paper by J. W. Shirley, Binary numeration before Leibniz, Amer. J. Physics 19 (8) (1951), 452-454, contains an interesting look at some mathematics which appears in the hand written papers of Thomas Harriot [1560-1621]. Using the photographs of the two original Harriot manuscript pages reproduced in Shirley’s paper, we explain how Harriot was doing arithmetic with binary numbers.

Leibniz [1646-1716] is credited with the invention [1679-1703] of binary arithmetic, that is arithmetic using base 2. Laplace wrote:-

Leibniz saw in his binary arithmetic the image of Creation. … He imagined the Unity represented God, and Zero the void; that the Supreme Being drew all beings from the void, just as unity and zero express all numbers in his system of numeration. This conception was so pleasing to Leibniz that he communicated it to the Jesuit, Grimaldi, president of the Chinese tribunal for mathematics, in the hope that this emblem of creation would convert the Emperor of China, who was very fond of the sciences …

However, Leibniz was certainly not the first person to think of doing arithmetic using numbers to base 2. Many years earlier Harriot had experimented with the idea of different number bases….

Axiomatic proofs we may categorize as 'syntactic', meaning that they concern only symbols and the derivation of one string of symbols from another, according to set rules. 'Semantic' proofs, on the other hand, differ from syntactic proofs in being based not only on symbols but on a non-symbolic, non-linguistic component, a domain of objects. If the sole paradigm of 'proof ' in mathematics is 'axiomatic proof ', in which to prove a formula means to deduce it from axioms using specified rules of inference, then Gödel indeed appears to have had the last word on the question of PA-consistency. But in addition to axiomatic proofs there is another kind of proof. In this paper I give a proof of PA's consistency based on a formal semantics for PA. To my knowledge, no semantic consistency proof of Peano arithmetic has yet been constructed.

The difference between 'semantic' and 'syntactic' theories is described by van Fraassen in his book The Scientific Image :

"The syntactic picture of a theory identifies it with a body of theorems, stated in one particular language chosen for the expression of that theory. This should be contrasted with the alternative of presenting a theory in the first instance by identifying a class of structures as its models. In this second, semantic, approach the language used to express the theory is neither basic nor unique; the same class of structures could well be described in radically different ways, each with its own limitations. The models occupy centre stage." (1980, p. 44)

Van Fraassen gives the example on p. 42 of a consistency proof in formal geometry that is based on a non-linguistic model. Suppose we wish to prove the consistency of the following geometric axioms:

A1. For any two lines, there is at most one point that lies on both.
A2. For any two points, there is exactly one line that lies on both.
A3. On every line there lie at least two points.

The following diagram shows the axioms to be consistent:

Figure 1

The consistency proof is not a 'syntactic' one, in which the consistency of A1-A3 is derived as a theorem of a deductive system, but is based on a non-linguistic structure. It is a semantic as opposed to a syntactic proof. The proof constructed in this paper, like van Fraassen's, is based on a non-linguistic component, not a diagram in this case but a physical domain of three-dimensional cube-shaped blocks. ….

… The semantics presented in this paper I call 'block semantics', for reasons that will become clear…. Block semantics is based on domains consisting of cube-shaped objects of the same size, e.g. children's wooden building blocks. These can be arranged either in a linear array or in a rectangular array, i.e. either in a row with no space between the blocks, or in a rectangle composed of rows and columns. A linear array can consist of a single block, and the order of individual blocks in a linear or rectangular array is irrelevant. Given three blocks A, B and C, the linear arrays ABC and BCA are indistinguishable. Two linear arrays can be joined together or concatenated into a single linear array, and a rectangle can be re-arranged or transformed into a linear array by successive concatenation of its rows. The result is called the 'linear transformation' of the rectangle. An essential characteristic of block semantics is that every domain of every block model is finite. In this respect it differs from Tarski’s semantics for first-order logic, which permits infinite domains. But although every block model is finite, there is no upper limit to the number of such models, nor to the size of their domains.

It should be emphasized that block models are physical models, the elements of which can be physically manipulated. Their manipulation differs in obvious and fundamental ways from the manipulation of symbols in formal axiomatic systems and in mathematics. For example the transformations described above, in which two linear arrays are joined together to form one array, or a rectangle of blocks is re-assembled into a linear array, are physical transformations not symbolic transformations. …"

Wednesday, December 21, 2011

"Poe’s tale established the modern paradigm (which, as it happens, Dashiell Hammett and John Huston followed) of the hermetically sealed fiction of cross and double-cross in which spirited antagonists pursue a prized artifact of dubious or uncertain value."

For one such artifact, the diamond rhombus formed by two equilateral triangles, see Osserman in this journal.

"The past decade has been an exciting one in the world of mathematics and a fabulous one (in the literal sense) for mathematicians, who saw themselves transformed from the frogs of fairy tales— regarded with a who-would-want-to-kiss-that aversion, when they were noticed at all— into fascinating royalty, portrayed on stage and screen….

An epistemological cut can be described as the production of homonyms. For example, the word orb in Ptolemaic cosmology and the same word in the Kepler’s system, albeit similar, designate two entities that have nothing in common: the first one, in the Ancients’ cosmology, is a crystal sphere to which stars are attached; orb, for Kepler, is an ellipsis whose sole material existence is the algorithm describing its path. A cut becomes major when all word of different eras change meaning. A case in point is the cut between polytheism and monotheism (Judaism): the word god or god takes an entirely different meaning, and this change affects all areas of a vision of the world. From the non created world of the Ancients, inhabited by eternal Gods, we pass on to a world created by a unique God, who is outside of his creation. This cut affects all areas of thinking. However, mythology, albeit separated from the new vision by the cut, survives as an enduring residue. Our sexual thinking, for example, is essential mythological, as proven by the endurance of the Oedipus complex or our cult of this ancient deity called Eros. Love is inherently tied to what Freud called the omnipotence of thought or magical thinking.

Of course, the quintessential major epistemological cut for us is the break effectuated by modern science in the 17th century. All the names are affected by it: however, who can claim he or she has been entirely purged of pre-scientific reasoning? Despite us living in a scientific universe, we all have our little mythologies, residues of an era before the major epistemological cut.

Any modeling of major epistemological cuts, or paradigm changes as Thomas Kuhn would have it, has therefore to account at the same time for a complete break with past names (that is, new visions of the world) as well as the survival of old names and mythologies.

"These passages suggest that the Form is a character or set of characters common to a number of things, i.e. the feature in reality which corresponds to a general word. But Plato also uses language which suggests not only that the forms exist separately (χωριστά ) from all the particulars, but also that each form is a peculiarly accurate or good particular of its own kind, i.e. the standard particular of the kind in question or the model (παράδειγμα ) [i.e. paradigm ] to which other particulars approximate….

… Both in the Republic and in the Sophist there is a strong suggestion that correct thinking is following out the connexions between Forms. The model is mathematical thinking, e.g. the proof given in the Meno that the square on the diagonal is double the original square in area."

Wednesday, April 27, 2011

"… a small set of undergraduates culminate their academic careers with a translation thesis. Ford is one such student, currently completing her edition of Euripides’ 'The Bacchae,' a Greek tragedy centered on the god Dionysus’ revenge against his mortal family."

"The guards return with Dionysus himself, disguised as his priest and the leader of the Asian maenads. Pentheus questions him, still not believing that Dionysus is a god. However, his questions reveal that he is deeply interested in the Dionysiac rites, which the stranger refuses to reveal fully to him. This greatly angers Pentheus, who has Dionysus locked up. However, being a god, he is quickly able to break free and creates more havoc, razing the palace of Pentheus to the ground in a giant earthquake and fire."

The illustration for the Crimson article formed part of a post in this journal, Paradigms Lost, on March 10—

Wednesday, March 9, 2011

"Incommensurable. It is a strange word. I wondered, why did Kuhn choose it? What was the attraction?

Here’s one clue. At the very end of 'The Road Since Structure,' a compendium of essays on Kuhn’s work, there is an interview with three Greek philosophers of science, Aristides Baltas, Kostas Gavroglu and Vassiliki Kindi. Kuhn provides a brief account of the historical origins of his idea. Here is the relevant segment of the interview.

T. KUHN: Look, 'incommensurability' is easy.

V. KINDI: You mean in mathematics?

T. KUHN: …When I was a bright high school mathematician and beginning to learn Calculus, somebody gave me—or maybe I asked for it because I’d heard about it—there was sort of a big two-volume Calculus book by, I can’t remember whom. And then I never really read it. I read the early parts of it. And early on it gives the proof of the irrationality of the square root of 2. And I thought it was beautiful. That was terribly exciting, and I learned what incommensurability was then and there. So, it was all ready for me, I mean, it was a metaphor but it got at nicely what I was after. So, that’s where I got it.

'It was all ready for me.' I thought, 'Wow.' The language was suggestive. I imagined √2 provocatively dressed, its lips rouged. But there was an unexpected surprise. The idea didn’t come from the physical sciences or philosophy or linguistics, but from mathematics ."

A footnote from Morris (no. 29)—

"Those who are familiar with the proof [of irrationality] certainly don’t want me to explain it here; likewise, those who are unfamiliar with it don’t want me to explain it here, either. There are many simple proofs in many histories of mathematics — E.T. Bell, Sir Thomas Heath, Morris Kline, etc., etc. Barry Mazur offers a proof in his book, 'Imagining Numbers (particularly the square root of minus fifteen),' New York, NY: Farrar, Straus and Giroux. 2003, 26ff. And there are two proofs in his essay, 'How Did Theaetetus Prove His Theorem?', available on Mazur’s Harvard Web site."

There may, actually, be a few who do want the proof. They may consult the sources Morris gives, or the excellent description by G.H. Hardy in A Mathematician's Apology , or, perhaps best of all for present purposes, the proof as described in a "sort of a big two-volume Calculus book" (perhaps the one Kuhn mentioned)… See page 6 and page 7 of Volume One of Richard Courant's classic Differential and Integral Calculus (second edition, 1937, reprinted many times through 1970, and again in a Wiley Classics Library Edition in 1988).

"I agree with one of the earlier commenters that this is a piece of fine literary work. And in response to some of those who have wondered 'WHAT IS THE POINT?!' of this essay, I would like to say: Must literature always answer that question for us (and as quickly and efficiently as possible)?"

For an excellent survey of the essay's historical context, see The Stanford Encyclopedia of Philosophy article

"Malcolm…. shows that the middle dialogues do indeed take Forms to be both universals and paradigms…. He shows that Plato's concern to explain how the truths of mathematics can indeed be true played an important role in his postulation of the Form as an Ideal Individual."

Other uses of the phrase "concrete universal"– Hegelian and/or theological– seem rather distant from the concerns of Plato and Wimsatt, and are best left to debates between Marxists and Catholics. (My own sympathies are with the Catholics.)

Two views of "the white itself" —

"So did God cause the big bang?
Overcome by metaphysical lassitude,
I finally reach over to my bookshelf
for The Devil's Bible.
Turning to Genesis I read:
'In the beginning
there was nothing.
And God said,
'Let there be light!'
And there was still nothing,
but now you could see it.'"
-- Jim Holt, Big-Bang Theology,
Slate's "High Concept" department

"The world was warm and white when I was born:
Beyond the windowpane the world was white,
A glaring whiteness in a leaded frame,
Yet warm as in the hearth and heart of light."
-- Delmore Schwartz

"The structuralist semiotician Algirdas Greimas introduced the semiotic square (which he adapted from the 'logical square' of scholastic philosophy) as a means of analysing paired concepts more fully (Greimas 1987,* xiv, 49). The semiotic square is intended to map the logical conjunctions and disjunctions relating key semantic features in a text. Fredric Jameson notes that 'the entire mechanism… is capable of generating at least ten conceivable positions out of a rudimentary binary opposition' (in Greimas 1987,* xiv). Whilst this suggests that the possibilities for signification in a semiotic system are richer than the either/or of binary logic, but that [sic] they are nevertheless subject to 'semiotic constraints' – 'deep structures' providing basic axes of signification."

The semiotic square has proven to be an influential concept not only in narrative theory but in the ideological criticism of Fredric Jameson, who uses the square as "a virtual map of conceptual closure, or better still, of the closure of ideology itself" ("Foreword"* xv). (For more on Jameson, see the [Purdue University] Jameson module on ideology.)

Greimas' schema is useful since it illustrates the full complexity of any given semantic term (seme). Greimas points out that any given seme entails its opposite or "contrary." "Life" (s1) for example is understood in relation to its contrary, "death" (s2). Rather than rest at this simple binary opposition (S), however, Greimas points out that the opposition, "life" and "death," suggests what Greimas terms a contradictory pair (-S), i.e., "not-life" (-s1) and "not-death" (-s2). We would therefore be left with the following semiotic square (Fig. 1):

As Jameson explains in the Foreword to Greimas' On Meaning, "-s1 and -s2"—which in this example are taken up by "not-death" and "not-life"—"are the simple negatives of the two dominant terms, but include far more than either: thus 'nonwhite' includes more than 'black,' 'nonmale' more than 'female'" (xiv); in our example, not-life would include more than merely death and not-death more than life.

"The Game in the Ship cannot be approached as a job, a vocation, a career, or a recreation. To the contrary, it is Life and Death itself at work there. In the Inner Game, we call the Game Dhum Welur, the Mind of God."

Click on either of the logos below for religious meditations– on the left, a Jewish meditation from the Conference of Catholic Bishops; on the right, an Aryan meditation from Stormfront.org.

Both logos represent different embodiments of the "story theory" of truth, as opposed to the "diamond theory" of truth. Both logos claim, in their own ways, to represent the eternal Logos of the Christian religion. I personally prefer the "diamond theory" of truth, represented by the logo below.

“Thine, O LORD is the greatness, and the power, and the glory, and the victory, and the majesty: for all that is in the heaven and in the earth is thine; thine is the kingdom, O LORD, and thou art exalted as head above all.”

This verse is sometimes cited as influencing the Protestant conclusion of the Lord’s Prayer:

“Thine is the kingdom, and the power, and the glory, forever” (Mt 6.13b; compare 1 Chr 29.11-13)….

This traditional epilogue to the Lord’s prayer protects the petition for the coming of the kingdom from being understood as an exorcism, which we derive from the Jewish prayer, the Kaddish, which belonged at the time to the synagogical liturgy.

The Pennsylvania Lottery on Christmas evening paired 173 with the beastly number 0666. The latter number suggests that perhaps being “understood as an exorcism” might not, in this case, be such a bad thing. What, therefore, might “173” have to do with exorcism? A search in the context of the phrase “language games” yields a reference to Wittgenstein’s Zettel, section 173:

Language-games give general guidelines of the application of language. Wittgenstein suggests that there are innumerably many language-games: innumerably many kinds of use of the components of language.24 The grammar of the language-game influences the possible relations of words, and things, within that game. But the players may modify the rules gradually. Some utterances within a given language-game are applications; others are ‘grammatical remarks’ or definitions of what is or should be possible. (Hence Wittgenstein’s remark, ‘Theology as grammar’25 – the grammar of religion.)

The idea of the ‘form of life’ is a reminder about even more basic phenomena. It is clearly bound up with the idea of language. (Language and ‘form of life’ are explicitly connected in four of the five passages from the Investigations in which the term ‘form of life’ appears.) Just as grammar is subject to change through language-uses, so ‘form of life’ is subject to change through changes in language. (The Copernican revolution is a paradigm case of this.) Nevertheless, ‘form of life’ expresses a deeper level of ‘agreement.’ It is the level of ‘what has to be accepted, the given.’26 This is an agreement prior to agreement in opinions and decisions. Not everything can be doubted or judged at once.

This suggests that ‘form of life’ does not denote static phenomena of fixed scope. Rather, it serves to remind us of the general need for context in our activity of meaning. But the context of our meaning is a constantly changing mosaic involving both broad strokes and fine-grained distinctions.

The more commonly understood point of the ‘Private Language Argument’ – concerning the root of meaning in something public – comes into play here. But it is important to show just what public phenomenon Wittgenstein has in mind. He remarks: ‘Only in the stream of thought and life do words have meaning.’27

24

Investigations, sec. 23.

25

Investigations, sec. 373; compare Zettel, sec. 717.

26

Investigations, p. 226e.

27

Zettel, sec. 173. The thought is expressed many times in similar words.

The ‘possibility of religion’ manifested itself in considerable reading of religious works, and this in a person who chose his reading matter very carefully. Drury’s recollections include conversations about Thomas à Kempis, Samuel Johnson’s Prayers, Karl Barth, and, many times, the New Testament, which Wittgenstein had clearly read often and thought about.25 Wittgenstein had also thought about what it would mean to be a Christian. Some time during the 1930s, he remarked to Drury: ‘There is a sense in which you and I are both Christians.’26 In this context it is certainly worth noting that he had for a time said the Lord’s Prayer each day.27

Wittgenstein’s last words were: ‘Tell them I’ve had a wonderful life!’28

Wednesday, September 19, 2007

“– …He did some equations that would make God cry for the sheer beauty of them. Take a look at this…. The sonofabitch set out equations that fit the data. Nobody believes they mean anything. Shit, when I back off, neither do I. But now and then, just once in a while… — He joined physical and mental events. In a unified mathematical field. — Yeah, that’s what I think he did. But the bastards in this department… bunch of goddamned positivists. Proof doesn’t mean a damned thing to them. Logical rigor, beauty, that damned perfection of something that works straight out, upside down, or sideways– they don’t give a damn.”

“By equating reality with the metaphysical abstraction ‘contingency’ and explaining his paradigm by reference to simple images of order, Kermode [but see note below] defines the realist novel not as one which attempts to get to grips with society or human nature, but one which, in providing the consolation of form,* makes the occasional concession to contingency….”

"Following the parade, a speech is given by Charles Williams, based on his book The Place of the Lion. Williams explains the true meaning of the word 'realism' in both philosophy and theology. His guard of honor, bayonets gleaming, is led by William of Ockham."

A review by John D. Burlinson of Charles Williams's novel The Place of the Lion:

"… a little extra reading regarding Abelard's take on 'universals' might add a little extra spice– since Abelard is the subject of the heroine's … doctoral dissertation. I'd suggest the article 'The Medieval Problem of Universals' in the online Stanford Encyclopedia of Philosophy."

"The development of logic in the schools and universities of western Europe between the eleventh and fifteenth centuries constituted a significant contribution to the history of philosophy. But no less significant was the influence of this development of logic on medieval theology. It provided the necessary conceptual apparatus for the systematization of theology. Abelard, Ockham, and Thomas Aquinas are paradigm cases of the extent to which logic played an active role in the systematic formulation of Christian theology. In fact, at certain points, for instance in modal logic, logical concepts were intimately related to theological problems, such as God's knowledge of future contingent truths."

That entry contains, in turn, a reference to the journal Subaltern Studies. According to a review of Reading Subaltern Studies,

"… the Subaltern Studies collective drew upon the Althusser who questioned the primacy of the subject…."

Munt also has something to say on "the primacy of the subject" —

"Poststructuralism, following particularly Michel Foucault, Jacques Derrida and Jacques Lacan, has ensured that 'the subject' is a cardinal category of contemporary thought; in any number of disciplines, it is one of the first concepts we teach to our undergraduates. But are we best served by continuing to insist on the intellectual primacy of the 'subject,' formulated as it has been within the negative paradigm of subjectivity as subjection?"

How about objectivity as objection?

I, for one, object strongly to "the Althusser who questioned the primacy of the subject."

This Althusser, a French Marxist philosopher by whom the late Michael Sprinker (Taking Lucifer Seriously) was strongly influenced, murdered his wife in 1980 and died ten years later in a lunatic asylum.

Monday, August 4, 2003

“I can’t resist but end by pointing out the irony of the doctrine of the Trinity as seen by gay eyes. Please don’t take what I say next too seriously. I don’t believe that gender is very important or that it is any more present in God than is ‘green-ness,’ however, I simply can’t resist.

The Trinity seems to be founded on the ecstatic love union of two male persons; the Father and the Son. If one takes this seriously it is incestuous pedophilia. There is no doubt that this union is generative (and so in the origin of the meaning ‘sexual’) in character, because from it bursts forth a third person: Holy Spirit; neuter in Greek, feminine in Hebrew! Whereas Islam detests the Catholic idea that the Blessed Virgin was ‘impregnated’ by God, as demeaning to the transcendence of God, the internal incestuous homosexuality that the doctrine of the Trinity amounts to should really offend more!

Any orthodox account of the inner life of God is at best highly uncongenial to the paradigm of the heterosexual nuclear family. Amusingly, the contemporary Magisterium fails to notice this and even attempts to use the doctrine of the procession of the Spirit from the Father and the Son to bolster its conventional championing of ‘male-female complementarity’ and the centrality of procreation to all authentically ‘self-giving’ relationships. Absurdities will never cease!”

Amen to the conclusion, at least.

The author of this meditation, “Pharsea,” is a “traditional Catholic” and advocate of the Latin Mass — just like Mel Gibson. One wonders how Gibson might react to Pharsea’s theology.

As for me… I always thought there was something queer about that religion.